# Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills

## TL;DR

This paper demonstrates that the large N limit of 4d $ ext{SU}(N)$ $ ext{N}=4$ Super-Yang-Mills theory on $S^3$ contains enough states to account for the entropy of certain BPS black holes in AdS$_5$, revealing complex structure and new physics insights.

## Contribution

It shows that the superconformal index at large N reproduces black hole entropy and uncovers a complex structure with multiple exponential contributions and Stokes lines.

## Key findings

- Superconformal index reproduces black hole entropy
- Large N limit exhibits multiple exponential contributions
- Presence of Stokes lines indicates new physics phenomena

## Abstract

We resolve a long-standing question: does the four-dimensional $\mathcal{N}=4$ SU(N) Super-Yang-Mills theory on $S^3$ at large N contain enough states to account for the entropy of rotating electrically-charged BPS black holes in AdS$_5$? Our answer is positive. We reconsider the large N limit of the superconformal index, using the Bethe Ansatz formulation, and find an exponentially large contribution which exactly reproduces the Bekenstein-Hawking entropy of the black holes of Gutowski-Reall. Besides, the large N limit exhibits a complicated structure, with many competing exponential contributions and Stokes lines, hinting at new physics.